. Field-book for railroad engineers. Containing formulas for laying out curves, determining frog angles, levelling, calculating earth-work, etc., etc., together with tables of radii, ordinates deflections, long chords, magnetic variation, logarithms, logarithmic and natural sines, tangents, etc., etc . Fig. 23. hxample. Given 7 = 30°, 6 = 130, to find Tan! R. Here h = 130^7=7° 30 7 = 15° 72 = 71. Problem. Given the angle of intersection KC B = 1 [Jig. 23). %nd the tangent A C = T, or the radius A 0 = R, to find C D -^ b. S
. Field-book for railroad engineers. Containing formulas for laying out curves, determining frog angles, levelling, calculating earth-work, etc., etc., together with tables of radii, ordinates deflections, long chords, magnetic variation, logarithms, logarithmic and natural sines, tangents, etc., etc . Fig. 23. hxample. Given 7 = 30°, 6 = 130, to find Tan! R. Here h = 130^7=7° 30 7 = 15° 72 = 71. Problem. Given the angle of intersection KC B = 1 [Jig. 23). %nd the tangent A C = T, or the radius A 0 = R, to find C D -^ b. Solution. If T is given, we have (§ 70) T = h cot. ^ 7, or 6 =T lot i/ .•.h= r tan. 17. If R is given, we have (§ 70) R = b cot. ^7 cot. |^7, or 6R eot ^ Jcot. i / ..b = R tan. ;J 7 tan. ^ 7. 50 CIRCULAR CURVES. Example. Given /= 27°, T= 600 or 7^ = 2499 lb, to IHere b = 600 tan. 6° 45 = 71 01, or i = tan. 6° 45tan. 13° 30 = 1 72. Problem. Given the angle of intersection I of two tangentA C and D C (fg. 24) to find the tangent point A of a curve, that shedpass through a point E, given by CD == a, D E =^ b, and the angle CD E Eig. 24. Solution. Produce DE to the curve at G, and dra^7 C 0 to the cen-tre 0. Denote DFbyc. Then in the right triangle CDF we have(Tab. X. U) DF= CD cos. CDF, or c = a cos. Denote the distance A D from D to the tangent point by x. Then, byGeometry, x^ = D E X D G. But D G = D F-\- FG = DF +EF=2DF—DE = 2c — b. Therefore, x^ = b{2c — b), and 5^ x = ^b{2c — b). Having thus found A Z), we have the tangent AC = AD -{• DC= X -\- a. Hence, R ox D may be found (^ 5 or § 11). If the point E is given by £^^and Ci/perpendicular to each other,a and b may be found from these lines. For a = C H -\- DH ^ (75+JE;77cot. iZ(Tab. X. 9). and6 =^DE = ^^i- MISCELLANEOUS PROBLEMS. 5i Example. Given I = 20° 16, a = 600, and 6 = 80, to find x andH. Here c = 600 cos. 10° 8 = 59064, 2 c - 6 = , and x =ySO X 110^28 = Then
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